SCMA Codebooks Design for Three Optimization Algorithms Based on Eisenstein Integer Unit Circle

Codebook design plays a crucial role in non-orthogonal sparse code multiple access technology. In this paper, a mother constellation constructed by the Eisenstein integer unit circle in the complex plane is proposed, and the power imbalance and dimensionality reduction are introduced into the codebook design. Three optimization algorithms are used to maximize the minimum Euclidean distance (MED) of superimposed codewords on the resource element as the objective function, and the optimal solution of the rotation angle is finally obtained, so as to obtain the three expected codebooks. Simulation results demonstrate that the proposed codebooks have smaller bit error rate (BER) and better performance than the four benchmark codebooks provided under the condition of a Gaussian channel.